Another refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for convex functions of several variables defined on simplices.     

A refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

Aequationes mathematicae - We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for simplices, based on the average values of a convex function over the...     

Dynamic Lone Pair Expression as Chemical Bonding Origin of Giant Phonon Anharmonicity in Thermoelectric InTe

Loosely bonded (“rattling”) atoms with s² lone pair electrons are usually associated with strong anharmonicity and unexpectedly low thermal conductivity, yet their detailed correlation remains largely unknown. Here we resolve this correlation in thermoelectric InTe by combining chemical bonding analysis, inelastic X-ray and neutron scattering, and first principles phonon calculations. We successfully probe soft low-lying transverse phonons dominated by large In¹⁺ z-axis motions, and their giant anharmonicity. We show that the highly anharmonic phonons arise from the dynamic lone pair expression with unstable occupied antibonding states induced by the covalency between delocalized In¹⁺ 5s² lone pair electrons and Te 5p states. This work pinpoints the microscopic origin of strong anharmonicity driven by rattling atoms with stereochemical lone pair activity, important for designing efficient materials for thermoelectric energy conversion.     

Chiral-at-Molybdenum – A Computational Study on N-Substituted cis-MoO2(nacnac)2

Cis-MoO₂(nacnac)₂ (nacnac=β-diketiminate) can be a viable chiral-at-metal catalyst when its two β-diketiminate (nacnac) ligands are N-substituted to prevent Λ⇌Δ racemization. Even simple methyl groups raise the barriers for racemization significantly for the Bailar, Rây-Dutt, Conte-Hippler, and Dhimba-Muller-Lammertsma (DML) twists to a respectable 28.5, 37.8, 30.5, and 25.1 kcal/mol, respectively, at ωB97X-D/6-311+G(2d,p) (LANL2DZ for Mo) including acetonitrile solvation. The lowest energy DML barrier increases to ΔG^o=27.4 kcal/mol with N-substituted t-butyl groups. The nacnac ligands’ electronic and steric components to the racemization barriers are discussed.     

Varieties fibred over abelian varieties with fibres of log general type

Let (X,B)$(X,B)$ be a complex projective klt pair, and let f:X→Z$f:X\to Z$ be a surjective morphism onto a normal projective variety with maximal albanese dimension such that _KX+B$K_X+B$ is relatively big over Z. We show that such pairs have good log minimal models.